Abstract
The present paper describes the genesis of a horseshoe vortex in the symmetry plane in front of a juncture. In contrast to a previous topological investigation, the presence of the obstacle is no longer physically modelled. Instead, the pressure gradient, induced by the obstacle, has been used to represent its influence. Consequently, the results of this investigation can be applied to any symmetrical flow above a flat plate.
The genesis of the vortical structure is analysed by using the theory of nonlinear differential equations and the bifurcation theory. In particular, the genesis of a horseshoe vortex can be described by the unfolding of the degenerate singularity resulting from a Jordan Normal Form with three vanishing eigenvalues and one linear term which is related to the adverse pressure gradient. The examination of this nonlinear dynamical system reveals that a horseshoe vortex emanates from a non-separating flow through two subsequent saddle-node bifurcations in different directions and the transition of a node into a focus located in the flow field.
